This study evaluates the tensile properties, including the tensile strength and elongation at break, and dynamic behavior, including shock absorption and vertical deformation, of an elastic rubber layer in synthetic sports surfaces produced using waste tire chips containing styrene-butadiene rubber (SBR). The primary variables of the investigation were the number of compactions, resin–rubber granule ratio, and curing conditions, such as aging, the temperature, and the relative humidity. The test results showed an increase in the tensile strength of the elastic rubber layer with recycled SBR as the number of compactions, resin–rubber granule ratio, curing period, and temperature increased, while the elongation at break was affected by the curing temperature and period. Shock absorption and vertical deformation decreased with an increasing resin–rubber granule ratio and number of compactions due to the increased hardness. However, these properties were not significantly affected by the curing conditions. Furthermore, the test results indicated that the curing temperature has a pronounced effect on the tensile properties of the elastic rubber layer, and maintaining the appropriate curing temperature—approximately 50 °C—is a possible solution for improving the relatively low tensile properties of the elastic rubber layer.